System.Data.SqlClient.SqlError: The backup of the file or filegroup "sysft_SearchCatalog" is not permitted because it is not online. BACKUP can be performed by using the FILEGROUP or FILE clauses to restrict the selection to include only online data. (Microsoft.SqlServer.Smo)

It’s because of your Full Text Catalog offline or the parameter incorrect. For my case, I used my local design path but this path doesn’t exist on live server and get the above error when backup. You can generate the sql query to view the source.

Solution: you can simply delete the catalog or rebuild it (expand your db > Storage > Full Text Catalog)